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Iterative methods for dense linear systems on distributed memory parallel computers

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1999年第3期E82A卷 483-486页

作者： Yokoyama, M Shigehara, T Mizoguchi, H Mishima, T Saitama Univ Dept Informat & Comp Sci Urawa Saitama 3388570 Japan

The Conjugate Residual method, one of the iterative methods for solving linear systems, is applied to the problems with a dense coefficient matrix on distributed memory parallel-computers. Based on an assumption on the computation and communication times of the proposed algorithm for parallel computers, it is shown that the optimal number of processing elements is proportional to the problem size N. The validity of the prediction is confirmed through numerical experiments on Hitachi SR2201.

关键词： iterative methods for solving dense linear systems the conjugate gradient method the conjugate residual method parallel processing distributed memory parallel computers

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On partitioning two dimensional finite difference meshes for distributed memory parallel computers

On partitioning two dimensional finite difference meshes for...

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22nd Euromicro International Conference on parallel, distributed, and Network-Based Processing (PDP)

作者： Grandjean, Anael Ucar, Bora Ecole Normale Super Lyon UMR CNRS INRIA UCBL F-69364 Lyon France Ecole Normale Super Lyon CNRS F-69364 Lyon France

ISBN: (纸本)9781479927289

We investigate the problem of partitioning finite difference meshes in two dimensions among the processors of a parallel computer. The objective is to achieve a perfect load balance while minimizing the communication cost. There are well-known graph, hypergraph, and geometry-based partitioning algorithms for this problem. The known geometric algorithms have linear running time and obtain the best results for very special mesh sizes and processor numbers. We propose another geometric algorithm. The proposed algorithm is linear;is applicable to much more cases than some well-known alternatives;obtains better results than the graph partitioning algorithms;obtains better results than the hypergraph partitioning algorithms almost always. Our algorithm also obtains better results than a known asymptotically-optimal algorithm for some small number of processors. We also catalog related theoretical results.

关键词： distributed processing finite difference methods graph theory mesh generation resource allocation distributed memory parallel computers geometry-based partitioning algorithms graph partitioning algorithms hypergraph partitioning algorithms linear running time perfect load balance two dimensional finite difference meshes Approximation algorithms Diamonds Measurement Partitioning algorithms Program processors Shape Standards

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Using distributed memory parallel computers and GPU clusters for multidimensional Monte Carlo integration

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CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE 2015年第4期27卷 923-936页

作者： Szalkowski, Dominik Stpiczynski, Przemyslaw Marie Curie Sklodowska Univ Inst Math PL-20031 Lublin Poland

The aim of this paper is to show that the multidimensional Monte Carlo integration can be efficiently implemented on various distributed memory parallel computers and clusters of multicore nodes using recently developed parallel versions of linear congruential generator and lagged Fibonacci generator pseudorandom number generators. We show how to accelerate the overall performance by offloading some computations to Graphics Processing Units (GPUs), and we discuss how to transform Message Passing Interface (MPI)+OpenMP programs to MPI+OpenMP+CUDA model. We explain how to utilize multiple cores of CPUs together with multiple GPU accelerators within a single node and how to achieve reasonable load balancing of all computational resources of GPU-accelerated multicore nodes. We present and discuss the results of experiments performed on the following target architectures: IBM Blue Gene/Q parallel computer, a cluster of Intel Xeon E5-2660 servers, and a Tesla-based GPU cluster with Intel Xeon X5650 multicore processors. The results are presented from two points of view: strong scaling and weak scaling. We also compare the performance of all considered architectures. Copyright (c) 2014 John Wiley & Sons, Ltd.

关键词： multidimensional integration Monte Carlo methods parallelized pseudorandom number generators linear congruential generator lagged Fibonacci generator distributed memory parallel computers GPU clusters efficiency scalability

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Iterative solution of elliptic collocation systems on a cognitive parallel computer

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computers & MATHEMATICS WITH APPLICATIONS 2004年第5-6期48卷 951-970页

作者： Mathioudakis, EN Papadopoulou, EP Saridakis, YG Tech Univ Crete App Math & Comp Lab Khania 73100 Greece

The performance of parallel algorithms implementing the block SOR iterative method, used for the solution of linear systems arising from the discretization of elliptic BVPs by the finite element collocation method, is investigated in this paper. By making use of a recently introduced block tridiagonal partitioning of the collocation matrix, which yields faster rates of convergence, and its associated modified red-black ordering of unknowns and equations, we succeeded to increase the scalability of the problem. The study of the communicational and computational needs of the problem on a virtual parallel machine made possible the mapping of the resulted SOR-algorithm on a fixed size distributed memory parallel system, utilizing a simple pipeline architecture among its processors, in an optimum way. The proposed parallel schemes are being realized on a Parsytec cognitive computer via an SPMD programming model. Speedup measurements are used to reveal the efficiency of our implementation. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： successive overrelaxation (SOR) collocation red-black orderings distributed memory parallel computers MIMD SPMD cognitive computers

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Memetic algorithms for parallel code optimization

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INTERNATIONAL JOURNAL OF parallel PROGRAMMING 2007年第1期35卷 33-61页

作者： Oezcan, Ender Onbasioglu, Esin Yeditepe Univ TR-34755 Istanbul Turkey

Discovering the optimum number of processors and the distribution of data on distributed memory parallel computers for a given algorithm is a demanding task. A memetic algorithm (MA) is proposed here to find the best number of processors and the best data distribution method to be used for each stage of a parallel program. Steady state memetic algorithm is compared with transgenerational memetic algorithm using different crossover operators and hill-climbing methods. A self-adaptive MA is also implemented, based on a multimeme strategy. All the experiments are carried out on computationally intensive, communication intensive, and mixed problem instances. The MA performs successfully for the illustrative problem instances.

关键词： distributed memory parallel computers memetic algorithms parallelizing compilers search methods

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Software cache techniques for memory nodes in distributed memory parallel production systems

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 1996年第8期E79D卷 1046-1054页

作者： Miyazaki, J Yokota, H School of Information Science Japan Advanced Institute of Science and Technology Hokuriku Ishikawa-ken 923-12 Japan

Because the match phase in OPS5-type production systems requires most of the system's execution time and memory accesses, we proposed hash-based parallel production systems, CPPS (Clustered parallel Production Systems), based on the RETE algorithm for distributed memory parallel computers, or multicomputers to reduce such a bottleneck. CPPS was effective in speeding up the match phase, but still left room for optimizations. In this paper, we introduce software cache techniques to memory nodes in the CPPS as one of the optimizations, and implement it on a multicomputer, nCUBE2. The benchmark results show that the CPPS with the software cache is about 2-fold faster than the original, and more than 7-fold faster than the simple hash method proposed by Acharya et al. for a large scale problem. The speed-up can be attributed to decreased communication costs.

关键词： distributed memory parallel computers production systems software cache techniques load balancing

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Dynamic partitioning of non uniform structured workloads with spacefilling curves

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IEEE TRANSACTIONS ON parallel AND distributed SYSTEMS 1996年第3期7卷 288-300页

作者： Pilkington, JR Baden, SB Computer Science and Engineering Department University of California La Jolla CA USA

We discuss Inverse Spacefilling Partitioning (ISP), a partitioning strategy for non-uniform scientific computations running on distributed memory MIMD parallel computers. We consider the case of a dynamic workload distributed on a uniform mesh, and compare ISP against Orthogonal Recursive Bisection (ORE) and a Median of Medians variant of ORE, ORB-MM. We present two results. First, ISP and ORB-MM are superior to ORE in rendering balanced workloads-because they are more fine-grained-and incur communication overheads that are comparable to ORE. Second, ISP is more attractive than ORB-MM from a software engineering standpoint because ii avoids elaborate bookkeeping. Whereas ISP partitionings can be described succinctly as logically contiguous segments of the line, ORB-MM's partitionings are inherently unstructured. We describe the general d-dimensional ISP algorithm and report empirical results with two- and three-dimensional, non-hierarchical particle methods.

关键词： dynamic load balancing distributed memory parallel computers spacefilling curve non-uniform computations irregular data partitioning particle methods performance

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Efficient implementation of multi-dimensional array redistribution

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 1998年第11期E81D卷 1195-1204页

作者： Guo, MY Yamashita, N Nakata, I Univ Tsukuba Doctoral Program Engn Tsukuba Ibaraki 3050006 Japan

Array redistribution is required very often in programs on distributed memory parallel computers. It is essential to use efficient algorithms for redistribution, otherwise the performance of programs may degrade considerably. In this paper, we focus on automatic generation of communication routines for multi-dimensional redistribution. The principal advantage of this work is to gain the ability to handle redistribution between arbitrary source and destination processor sets and between arbitrary source and destination distribution schemes. We have implemented these algorithms using parallelware communication library. Some experimental results show the efficiency and flexibility of our techniques compared to the other redistribution works.

关键词： parallelizing compiler array redistribution distributed memory parallel computers interprocessor communication data parallel language

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Mapping finite element grids onto parallel multicomputers using a self-organising map

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IEE PROCEEDINGS-computers AND DIGITAL TECHNIQUES 1998年第3期145卷 211-214页

作者： Tan, RS Narasimhan, VL Stanford Univ Dept Elect Engn Stanford CA 94305 USA Def Sci & Technol Org Salisbury SA 5108 Australia

LSOM (load-balancing self-organising map), a neural network based on Kohonen's self-organising map, is proposed for the problem of mapping finite element method (FEM) grids to distributed memory parallel computers with mesh interconnection networks. The rough global ordering produced by LSOM is combined with the local refinement Kernighan-Lin algorithm (LSOM-KL) to obtain the solution. LSOM-KL achieved a load imbalance of less than 0.1% and a low number of hops, comparable to results obtained with commonly used recursive bisection methods.

关键词： neural network self-organising map finite element method distributed memory parallel computers

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A methodology for devising optimal all-port all-to-all broadcast algorithms in 2-dimensional tori 28

A methodology for devising optimal all-port all-to-all broad...

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28th Annual IEEE International Conference on Local Computer Networks held in conjunction with Workshop on High-Speed Local Networks/Workshop on Wireless Local Networks

作者： Jung, JP Sakho, I Univ Metz UFR MIM F-57035 Metz 01 France

ISBN: (纸本)0769520375

All-to-all broadcast is a collective communication in a network with the constraint that every node must send to each other certain piece of its data. This paper reports a methodology to devise all-port efficient algorithms for such communication in multidimensional tori. Efficiency criteria being minimum steps of no duplicated data exchange while balancing the communication links-load. Resulting algorithms are message combining algorithms. To complete an all-to-all broadcast these algorithms require the number of data exchange steps in terms of link hops to be equal to the diameter of the interconnection network The number of data exchanged at each step varies as a gaussian curve whose maximum equals the half of the network diameter per link.

关键词： distributed memory parallel computers multidimensional tori all-to-all broadcast NODUP store-and-forward routing message combining

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